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A Problem with Simplify

  • To: mathgroup at smc.vnet.net
  • Subject: [mg87419] A Problem with Simplify
  • From: "Kevin J. McCann" <Kevin.McCann at umbc.edu>
  • Date: Thu, 10 Apr 2008 02:12:11 -0400 (EDT)
  • Organization: University System of Maryland

I have the following rather simple integral of two sines, which should 
evaluate to zero if m is not equal to n and to L/2 if they are the same.

The following is just fine

Imn = Simplify[Integrate[
        Sin[(m*Pi*x)/L]*
          Sin[(n*Pi*x)/L],
        {x, 0, L}]]


However, if I specify that m and n are integers, I only get the 
"general" solution of zero, i.e. when m and n are not equal.

Imn = Simplify[Integrate[
        Sin[(m*Pi*x)/L]*
          Sin[(n*Pi*x)/L],
        {x, 0, L}],
      Element[m, Integers] &&
        Element[n, Integers]]

The workaround is obvious in this case, but shouldn't mma give multiple 
answers? Perhaps something similar to what it already does with Integrate?

Kevin
-- 

Kevin J. McCann
Research Associate Professor
JCET/Physics
Physics Building
University of Maryland, Baltimore County
1000 Hilltop Circle
Baltimore, MD 21250


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